{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Auditory Sound Processing - Part IIb: Effect of Windowing\n",
    "\n",
    "author: Thomas Haslwanter\\\n",
    "date: April-2020\n",
    "\n",
    "This notebook gives an example of windowing, showing that:\n",
    "* selection of a narrower time-window widens the frequncy spectrum\n",
    "* application of a *window function* eliminates ripples in the frequency spectrum"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Function definitions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "# Standard packages\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def powerSpect(data, sampleRate):\n",
    "    '''Powerspectrum, calculated via Fourier Transfrom'''\n",
    "    \n",
    "    nData = len(data)\n",
    "    fftData = np.fft.fft(data)\n",
    "    \n",
    "    Pxx = np.real(fftData * fftData.conj()) / nData\n",
    "    freq = np.arange(nData)*sampleRate / nData\n",
    "    \n",
    "    return (Pxx, freq)\n",
    "    \n",
    "def showData(samplingRate, x, titleText):\n",
    "    '''Show data in time domain, and corresponding powerspectrum'''\n",
    "    \n",
    "    t = np.arange(len(x)) / samplingRate\n",
    "        \n",
    "    fig, axs = plt.subplots(2,1)\n",
    "    axs[0].plot(t,x)\n",
    "    axs[0].set_xlabel('Time [s]')\n",
    "    axs[0].set_ylabel('Signal')\n",
    "    axs[0].set_title(titleText)\n",
    "    \n",
    "    # Calculate the powerspectrum\n",
    "    (Pxx, freq) = powerSpect(x, samplingRate)\n",
    "    \n",
    "    axs[1].plot(freq, Pxx, 'o-')\n",
    "    axs[1].set_xlim(1, 5000)\n",
    "    axs[1].set_xlabel('Frequency [Hz]')\n",
    "    axs[1].set_ylabel('Power')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create a Sine Wave"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "# Set the parameters\n",
    "sampleRate = 100000\n",
    "dt = 1./sampleRate\n",
    "f = 1000\n",
    "tMax = 0.01\n",
    "\n",
    "# Calculate the data\n",
    "t = np.arange(0, tMax, dt)\n",
    "x = np.sin(2*np.pi*f*t)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1) Original Data, 2) Clipped Data, and 3) Clipped & Windowed Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "showData(sampleRate, x, 'Cosine wave')\n",
    "\n",
    "# Clip the data\n",
    "y = x\n",
    "y[1:199] = 0\n",
    "y[400:1001] = 0\n",
    "showData(sampleRate, y, 'Clipped Signal')\n",
    "\n",
    "# Window the clipped data\n",
    "z = y;\n",
    "window = np.hamming(201)\n",
    "z[199:400] = z[199:400]*window\n",
    "showData(sampleRate, z, 'Clipped & Windowed Signal')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[9_Soundproc_TimeDependence](9_Soundproc_TimeDependence.ipynb)<img src=\"data\\images\\Forward_Backward.png\" align='middle'>[10_ControlSystems](10_ControlSystems.ipynb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
